Graph Iterated Function Systems and Fractal Tops
Dynamical Systems
2024-02-05 v2
Abstract
Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces. For the simplest overlapping interval IFS, we find a sufficient condition for the closure of its tops code space to be a shift space of finite type. Likewise, we find that shift invariance properties do not directly extend to the graph-directed setting.
Cite
@article{arxiv.2402.00237,
title = {Graph Iterated Function Systems and Fractal Tops},
author = {Grover Lancaster-Cole and Georgiana Lyall and Thomas Malcolm and Qiyu Zhou},
journal= {arXiv preprint arXiv:2402.00237},
year = {2024}
}
Comments
19 pages, 6 figures